/usr/share/acl2-4.3/books/str/arithmetic.lisp is in acl2-books-source 4.3-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 | ; ACL2 String Library
; Copyright (C) 2009-2010 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version. This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
; more details. You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "ACL2")
(include-book "arithmetic/top" :dir :system)
(include-book "unicode/nthcdr" :dir :system)
(include-book "unicode/append" :dir :system)
(include-book "unicode/repeat" :dir :system)
(in-theory (enable acl2::make-list-ac->repeat))
;; This whole file is a "bozo" that we should consider moving elsewhere.
(defthm negative-when-natp
(implies (natp x) (equal (< x 0) nil)))
(defthm eqlablep-when-characterp
(implies (characterp x) (eqlablep x)))
(defthm len-zero
(equal (equal 0 (len x))
(not (consp x))))
(defthm nth-of-len
(equal (nth (len x) x)
nil))
(defthm nth-when-bigger
(implies (<= (len x) (nfix n))
(equal (nth n x)
nil))
:hints(("Goal" :in-theory (enable nth))))
(defthm character-listp-of-repeat
(implies (characterp x)
(character-listp (acl2::repeat x n)))
:hints(("Goal" :in-theory (enable acl2::repeat))))
(defthm len-of-append
(equal (len (append x y))
(+ (len x)
(len y))))
(defthm consp-of-repeat
(equal (consp (acl2::repeat x n))
(not (zp n)))
:hints(("Goal" :in-theory (enable acl2::repeat))))
(defthm car-of-append
(equal (car (append x y))
(if (consp x)
(car x)
(car y))))
(defthm car-of-repeat
(equal (car (acl2::repeat x n))
(if (zp n)
nil
x))
:hints(("Goal" :in-theory (enable acl2::repeat))))
(defthm append-of-repeat-to-cons-of-same
(equal (append (acl2::repeat a n) (cons a x))
(cons a (append (acl2::repeat a n) x)))
:hints(("Goal" :in-theory (enable acl2::repeat))))
(defthm len-of-nonempty-string-is-positive
(implies (and (stringp x)
(not (equal x "")))
(< 0 (len (coerce x 'list))))
:hints(("Goal"
:in-theory (disable coerce-inverse-2)
:use ((:instance coerce-inverse-2)))))
(defthm simpler-take-of-len
(equal (simpler-take (len x) x)
(list-fix x))
:hints(("Goal" :in-theory (enable simpler-take))))
(defthm simpler-take-of-zero
(equal (simpler-take 0 x)
nil)
:hints(("Goal" :in-theory (enable simpler-take))))
(defthm character-listp-of-simpler-take
(implies (character-listp x)
(equal (character-listp (simpler-take n x))
(<= (nfix n) (len x))))
:hints(("Goal" :in-theory (enable simpler-take))))
(defthm subsetp-equal-of-cons-right
(implies (subsetp-equal x y)
(subsetp-equal x (cons b y))))
(defthm subsetp-equal-reflexive
(subsetp-equal x x))
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